'Unless' is 'Or', Unless '¬A Unless A' is Invalid

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Roy Cook


The proper translation of "unless" into intuitionistic formalisms is examined. After a brief examination of intuitionistic writings on "unless", and on translation in general, and a close examination of Dummett's use of "unless" in Elements of Intuitionism (1975b), I argue that the correct intuitionistic translation of "A unless B" is no stronger than "-B -> A". In particular, "unless" is demonstrably weaker than disjunction. I conclude with some observations regarding how this shows that one's choice of logic is methodologically prior to translation from informal natural language to formal systems.

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Cook, R. (2022). ’Unless’ is ’Or’, Unless ’¬A Unless A’ is Invalid. Dialectica, 999(1). https://doi.org/10.48106/dial.v74.i2.07